On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

The symmetry properties of the mono- and bielectronic terms contributing to the Fock matrix in the ab initio Hartree–Fock treatment of periodic systems are discussed. A computational scheme which takes full advantage of the point symmetry is presented; in this respect, it represents a generalization of the scheme proposed in Int. J. Quantum Chem. 17 , 501 (1980). Computational details and numerical examples are reported; it is shown that with respect to two of the bottlenecks of this kind of calculation, namely, computer time and backing storage required for the bielectronic integrals, it is possible to obtain saving factors as large as h and h², respectively, where h is the order of the point group. Preliminary tests are reported which indicate that the study of relatively complicated systems, like quartz or corundum (9 and 10 atoms in the unit cell, respectively) at an ab initio Hartree–Fock level is now within reach.